Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
928 conjugacy classes of subgroups; only the 405 normal subgroups are shown.
This group has 928 conjugacy classes of subgroups — too many to draw. Only its 405 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D61 |
| commutator | C22×C61 | C23×C4 |
| Frattini | C23 | C23×D61 |
| Fitting | C23×Q8×C61 | C2 |
| socle | C24×C61 | C23 |
| hypercenter | C23×Q8 | D61 |
| hypocenter | C61 | C2×#391 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C24 ◁ C23×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #16839669 | C2 | direct (N × H) |
| 15. C22×Q8×C61 | C4 | semidirect |
| 23. C2×Q8×C61 | C2×C4 | semidirect |
| 36. C22×Dic61 | Q8 | semidirect |
| 62. C2×Dic61 | C2×Q8 | semidirect |
| 78. C2×C61 | #391 | semidirect |
| 89. C61 | C2×#391 | semidirect |
| 92. C22×Q8 | Dic61 | semidirect |
| 107. C2×Q8 | C2×Dic61 | semidirect |
| 161. C2 | #16839669 | direct (N × H) |